数学内容审查二世

让我们开始谈论顶部初等代数概念上你会看到数学的行为。我们将谈论替代变量,简化方程,求解线性方程组和不等式。如果你想,“噢,我的天哪,这听起来真的压倒性的,“别担心我们会分手。
让我们开始讨论替代变量。这些问题给你一个代数方程,然后一个变量的值内,他们将插进去就可以了。这些是直接的。让我们看看这个,看起来复杂,当你第一次看,但仔细看,当x + y是3,的值是多少两次括号x + y + x + y / 3 -括号x + y的四次方。所以它看起来可怕,但我们知道,我们知道x + y等于三,现在这个情况你就塞在无论你看到x + y。所以它变成了一个非常简单的问题,我们有两个乘以三,像x + y, + 3 /三个还是一个,- 3的第四,好了好了。简化,这是6 + 1 - 81,好吧,这等于6,7 - 81 - 74,我们有它。这不是坏,答案将是正确的选择。
让我们继续。让我们看看简化方程,所以x²- 4 x + 9在括号和另一个括号,我们有三个x²- 2 x - 6。看起来很复杂,你想,“噢,我的天哪,有乘法,括号。”But if you take a close look, all we doing is subtracting, so these question types are just testing, can you combine expressions. These you remember from algebra, you know in school, combining like terms. So let's go ahead and get started with this problem. So we're going to get rid of the parenthesis, x minus four x plus nine, and now the next part, students often mess up on this so keep an eye out. You want to distribute your negative, it is so important it needs to go to every one of your terms, because your parenthesis means that, it's got to travel to every one of the parts. So minus three x squared, plus two x 'cause you've got two negatives there, so plus two x and then also plus six, great. And now this is looking pretty straight forward right? And now you know you just have to combine like terms, which you probably remember doing you know from class. So we've got x squared minus three x squared, okay just negative two x squared, so let's cross this out this becomes negative two x squared. Next you've got your negative four x plus two x, so negative four x plus two x just negative two x, and I can cross these out too. Okay last, nine plus six just 15, and we've got it. We've just simplified these expressions perfect. So which of these choices matches this? We need negative two x squared minus two x plus 15, and C is the correct answer choice here.
让我们继续,下一个解线性方程。又很直接但值得回顾。如果5 x + 3 = 23日12 x - 10是什么?所以线性方程是非常直接的,你知道我们不是说x², x立方,只是一个普通的x,往往只是一个变量,你要做什么,你要找出x是什么吗?5 x + 3是23,然后还有一个步骤,那么12 x - 10。所以你把它变成部分,如果5 x + 3是23,首先x是什么?所以5 x + 3 = 23,你知道你需要孤立的变量,我们要三到另一边,所以我们5 x = 20。在这种情况下x等于四,对吧?因为你两边同时除以5。好吧,但是我们没有做,顺便说一下你们小费,偶尔的人实际上意味着一种答案的选择,答案,你会得到第一一半的问题,如果这是一个两部分的问题。 So keep an eye out, here they're nice, we don't have a four, but sometimes there might be. Okay we know we're not done, we need to plug in our four to our x, back into 12 x minus ten, let's do that, so 12 times four minus ten, okay we know we do our multiplication before a subtraction, 48 minus ten which is going to equal 38. So B is the correct answer choice here. And you see how even though this looked you know, a couple of steps maybe a little tricky, it's really pretty straight forward if you remember the stuff you learn in school about isolating your variable.
让我们继续看看不平等。这些都是我最喜欢的一个话题代数。这一不平等状态方程的一面大于另一个。检查标志意味着什么,如果你有一个,这是一个小于B,如果你有,我的老师我想是五年级,想一想你可能有这个,她说,鳄鱼吃更大的方面你知道,如果你有一个开口,就指着大等式的一部分,这就是我记住它,因为嘴巴是指向B, B是大,所以一个小于B, A比B, A是小于或等于B如果你有这条线,和一个大于或等于B,好吧只是一个快速回顾。
让我们做一个问题,现在让我告诉你一些重要的事情,这些看起来有点吓人,但实际上他们如何做一个直接的代数问题,假装这是一个等号。一切皆会改变是唯一一次如果乘以或除以一个负数,看这个,他们测试这个行为,在这种情况下,你要翻你的不平等。好了,如果四次x - 3 - 2,是更大的,好让我写出来,4乘以x - 3 - 2大于或等于4 x + 5的三倍。好吧,让我们做如何做一个典型的方程,一次又一次你要什么孤立的变量我们移动一些东西。首先,你知道你需要解决括号,所以我们要做4 x - 12和分发4 x - 12 - 2大于或等于12 x + 15。好,这已经是简单,现在你知道这是结束,这结束了,四个x - 14日14大于或等于12 x + 15,现在我们可以把14个其他符号,然后我们可以把12 x的一面。我们来做,与此同时,我们有12 x移动,所以你会,14 - 8 x和,如果你将这一边和你添加它,你要大于或等于29。好的我们几乎完成了,现在我们要做的是两边除以- 8。是的我说-,我们除以一个负数,所以我们要改变不平等和这样,除以- 8,除以- 8。现在x小于或等于,我翻转它,比29 - 8。 And actually you can't simplify that any further because 29 is prime. Great, which answer choice looks like that, and we see it's answer choice D, x is less than or equal to 29 over negative eight. And be careful because always one of the answer choices will be the same answer if you didn't flip the inequality, okay.
它的顶部初等代数题目你会看到在行动。又有十个这样的,您将看到在数学部分。现在如果你还觉得你需要一点工作没问题,头奖金材料,你会发现有很多资源和额外的实践问题。
中级代数。这是两个概念,你会看到出现最频繁的中级代数法,记住有九个中级代数问题。首先解二次方程,然后求解系统方程我们就去。让我们从第一个开始二次方程。希望你们记住这些是数学课。这一个方程是平方,他们通常以AX²+ BX + C,这当你把它们与你的两套括号和你找到解决方案。让我告诉你一件事,实际上非常整洁的计算器有一个很好的项目,将为您计算。学生不知道项目在德州仪器计算器测试但他们是好的。所以检查你的奖金材料和我有一个项目,将为你做这个方程中所有你要做的就是把数字出现在他们每个人。这里没有你把数量1你把4、你会把四个,你做锤头公羊turup,第二个计算你扎根不需要脑力。
但是以防让我们来看一个例子,你会做手工。我们有一个真正的问题在这里X平方减去三等于两个X找到解决方案。好了我们正在寻找的可能值x,如果你看这个,你想哈看起来并不完全正确的记住你不能因素,除非它等于零说所以我们需要移动这一点。做一下第一所以我们有X的平方减去三个我们会减去两个X到另一边等于零。现在仍然没有好,因为你想要的形式你知道AX²+或- BX +或- C数量出现第三和附着在X出现第二次。开关这个- 3,- 2 X是一样的- 2 X - 3让我们写出来。X²- 2 X - 3 = 0。现在我们可以因素我们会把我们的两套括号好我们两边各有一个X。所以你记得从学校如果你有一个-,-你在实际方程了解会发生什么在你的括号?它不会是一个+和+的原因,给予你们所有人除了对吧? And it's not going to be a minus and a minus 'cause when you multiply negatives you also just get pluses. You're going to need one of these to be adding and one of these to be subtracting. So one of these is going to be a plus, one of these is going to be a minus. Remember when you're filling this out you're looking for two numbers that will multiply together to give you negative three, but add to give you negative two. Let's think about it for a second what about one and three? Let's say if you had one and three they combine to give you three and they would add to give you or subtract to give you two. The question is what's going to go where? Let's try to have you've got your three here and your one here and let's see how that would work. So we'd have X squared minus X plus three X that would give us a positive two X so that's not the right way to do it. We want to flip these and have the one appearing here and the three appearing here. Let's try it again, so X plus one and X minus three and now when you think about it that works right? You'd have if you've worked it back you would have X squared minus three plus one X that's still negative two X minus three and that's perfect.
问题是我们不做有什么解决方案吗?我有很多学生,看看这个,他们会说你是一个- 3完美。犯那样的错误,因为你不知道总会有答案的选择,这是错误的。记住现在你知道X + 1和X - 3每一个等于零。所以如果你有X + 1 = 0 X可以- 1对吗?所以你的根是X = - 1。同时我们有X - 3 = 0 X等于三。所以我们两根是X = - 1, X等于三的这些数字吗?C - 1,我们想要积极三C将正确答案的选择。
解决好了下一个话题的系统方程。这是一个情况下你会有两个不同的问题,两个变量,它们都分享。Y = 5 X - 1,我们有两个Y = 6 X + 24那么你做什么呢?希望你记得从学校实际上有两种方法来解决这类问题。您可以使用替换实际上插入我们知道自5 X - Y是一个无处不在我们看到Y我们可以插入5 X - 1。还有你可能还记得这个所谓的组合排列你的方程和添加或减去,看看你是否可以划掉一个变量和解决。这里我要做的只是替换。奖金材料中会有一个很好的结合的例子,因为根据具体的情况你知道一件事情可能会更容易比其他但你总能做的策略。这里让我们用更简单,因为它只是很直接,Y = 5 X - 1 Y我们可以代入。这两次5 X - 1 = 6 X + 24。 And now we can just simplify so we know ten X minus two is equal to six X plus twenty four. So if you move the six X over here and the two over here let's see you would have that four X 'cause we're subtracting, the six X, four X is equal adding the two over here to 26 and therefore X is equal to 26 over four which simplifies right? It simplifies to 13 halves. And there we go D is the correct answer choice here.
让我们来总结一下这节课中我们讨论了初等代数和我们谈论中级代数。有一个单独的事件,处理算术。所以你看代数法是一个非常大的话题,我想让你花了很多时间去练习你的奖金材料如果他们任何的话题,你觉得你需要更多的练习。